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%% lecture25.tex
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%% Started on  Thu Jan  5 08:33:18 2012 alex
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\exercises
\begin{xca}
Calculate the cohomology ring with coefficients in $\ZZ_2$ for
Klein bottle\index{Klein Bottle!Cohomology of ---}.
\end{xca}
\begin{xca}
Let $f$ denote a map of a sphere with $g$ handles into a sphere
with $h$ handles where $g<h$. Prove that the degree of $f$ is
equal to zero.

\textsc{Hint:} Consider homomorphism of cohomology rings. Start
with the analysis of the case $g=0$.
\end{xca}
